Bohmian mechanics in the exact factorization of electron-nuclear wavefunction

TL;DR

This paper explores how Bohmian mechanics can be applied to the exact factorization approach of electron-nuclear wavefunctions, demonstrating that classical trajectories influenced by the quantum potential can replicate quantum nuclear dynamics in strong-field processes.

Contribution

It introduces a method to use Bohmian mechanics with the exact nuclear TDSE to reproduce quantum nuclear motion through classical trajectories in strong-field scenarios.

Findings

Classical trajectories with Bohmian quantum potential can replicate quantum dissociation dynamics.

The quantum potential significantly influences nuclear motion in strong-field processes.

The approach accurately models ionization and splitting of nuclear probability density.

Abstract

The exact factorization of an electron-nuclear wavefunction [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] allows us to define the rigorous nuclear time-dependent Schr\"{o}dinger equation (TDSE) with a time-dependent potential-energy surface (TDPES) that fully accounts for the coupling to the electronic motion and drives the nuclear wavepacket dynamics. Here, we study whether the propagation of multiple classical trajectories can reproduce the quantum nuclear motion in strong-field processes when their motions are governed by the quantum Hamilton-Jacobi equation derived by applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that multiple classical trajectories propagated by the force from the gradient of the exact TDPES plus the Bohmian quantum potential can reproduce the strong-field dissociation dynamics of a one-dimensional model of the H$_2^+$ molecule. Our results show that the force from the Bohmian quantum potential plays a non-negligible role in yielding quantum nuclear dynamics in the strong-field process studied here, where ionization and/or splitting of nuclear probability density occurs.